Comparison and choice: Relations between similarity processes and decision processes

Transcription

1 Psychonomic Bulletin & Review 1995, 2 (1), 1 19 Comparison and choice: Relations between similarity processes and decision processes DOUGLAS L. MEDIN Northwestern University, Evanston, Illinois ROBERT L. GOLDSTONE Indiana University, Bloomington, Indiana and ARTHUR B. MARKMAN Columbia University, New York, New York Research and theory in decision making and in similarity judgment have developed along parallel paths. We review and analyze phenomena in both domains that suggest that similarity processing and decision making share important correspondences. The parallels are explored at the level of empirical generalizations and underlying processing principles. Important component processes that are shared by similarity judgments and decision making include generation of alternatives, recruitment of reference points, dynamic weighting of aspects, creation of new descriptors, development of correspondences between items, and justification of judgment. INTRODUCTION My problem is that I have been persecuted by an integer. For seven years this number has followed me around, has intruded in my most private data, and has assaulted me from the pages of our most public journals (G. A. Miller, 1956, p. 81). So begins George Miller s classic paper on the magic number seven. Miller was intrigued by the observation that both immediate memory and absolute judgments appear to have the same capacity limitation (i.e., seven, plus or minus two, chunks of information). We, too, have been drawn to a parallel by what initially seemed to be coincidence but now forms a pattern of correspondences that we find difficult to dismiss. The domains in question are those of decision making and similarity judgments. So enamored are we of the correspondences that we have come to entertain the idea that decision making entails a similarity judgment. But we will begin with the more modest goal of convincing the reader that bringing these two domains of discourse together is even a good idea. Preparation of this article was supported by National Science Foundation Grants and We thank Lance Rips, Evan Heit, Jim Sherman, Edward Wisniewski, Dedre Gentner, Reid Hastie, two anonymous reviewers, and especially Hal Arkes for valuable advice, comments, and suggestions. The research described in this article conforms to the American Psychological Association ethical standards for research involving human participants. Correspondence concerning this article should be addressed to D. L. Medin, Psychology Department, Northwestern University, 2029 Sheridan Road, Evanston, IL ( medin@nwu.edu). To avoid later confusion, we need to insert some points and disclaimers. There are some pretty obvious senses in which similarity and decision making are related. It is trivially true that judging which of two objects is more like a third involves a decision; and it has long been known (e.g., Restle, 1961) that the similarity of alternatives affects choice. Our focus, however, is on the processing side of similarity, and we will treat similarity (comparison) as more like a verb than a noun. The fact that the similarity of alternatives influences decisions provides a clue to comparison processes, and it is these processes that are of interest. Finally, we are agnostic with respect to whether correspondences between similarity and decision making are unique to these domains. We believe that the parallels between these domains are worthy of investigation, even if other domains also exhibit similar correspondences. In fact, if the underlying common processes that we suggest are also shared by other aspects of cognition, such as attention and memory, our analysis will have additional import. Given the fundamental nature of similarity processes and decision processes, it would not be surprising if their shared aspects proved to be general properties of cognition. The process of categorization merits special consideration as potentially having important properties in common with similarity judgments and decision making. This is hardly surprising, given that many models for categorization are founded on similarity (for a review, see Goldstone, 1994a), and that several models of decision making are based on categorization (e.g., Kah- 1 Copyright 1995 Psychonomic Society, Inc.

2 2 MEDIN, GOLDSTONE, AND MARKMAN neman & D. T. Miller, 1986). Many of our specific proposals for common processes, such as dynamic weighting of properties, generation of new properties, and judgment justification, have also been recently developed in the categorization field (Murphy & Medin, 1985). It is not immediately obvious that similarity judgments and decision making have much in common. Furthermore, a quick review of typical paradigms from these two areas suggests further differences. Similarity judgments often involve either comparing two entities or judging which of a set of alternatives is most similar to some target or standard. Decision-making studies are frequently concerned with choices between options, where the outcome associated with an option may have some uncertainty associated with it. Three differences in these paradigms immediately suggest themselves: (1) There is no standard or target in decision-making studies; (2) similarity judgment seems to be importantly a function of shared or common properties, but in decision making, properties that options share may be irrelevant to the choice; and (3) there is no obvious analog in similarity of the probability dimension in risky choice. Are the above differences fatal to any deep correspondences between similarity judgments and decision making? For the moment, we offer three counterarguments; later on, we defend them. First of all, understanding the meaning or significance of the properties or aspects associated with a decision implicitly presupposes that some standard or ideal is used to determine their valence and magnitude. We will argue that decision tasks involve a standard that is implicit, or possibly explicit, and prestored, or possibly constructed. In doing so, we also address the issue of the role of common or shared properties. Given some standard, shared or common properties may arise either from comparing alternatives with each other or from comparing alternatives with the standard. Thus, for the second proposed difference, it remains to be seen whether the effects of shared properties on decision making and on similarity judgments are comparable. As for the third difference, for the moment, we will treat probability simply as another dimension along which choices may vary in similarity. We will argue, further, that the correspondences between similarity judgments and decision making are deep and provocative. Our review and analysis will describe the parallel course of development of these domains, building bridges between domains that have hitherto remained largely independent. Along the way, we will also suggest a number of new possible correspondences. Early research in both similarity judgments and decision making focused on the idea that subjects converted stimuli into some kind of common currency, such as utility in the case of decision making (e.g., Luce, 1959), or psychological distance in the case of similarity judgments (e.g., Shepard, 1962a, 1962b). In both areas, behavioral research soon demonstrated that a commoncurrency theory was limited in its ability to describe many phenomena. This research led to calls for the development of theories of the processes involved in making decisions and similarity comparisons, rather than settling for descriptive theories of the choices and judgments themselves (e.g., Tversky, 1972, 1977). We believe that this shared evolution is a function of more profound similarities between the domains. In the next section, we focus on parallel phenomena in each domain. There are several related strategies for carrying out this analysis. Certain phenomena may be common to both domains but more prominent and easier to analyze in one than in the other. If a phenomenon from one domain has not been studied in the other, the opportunity exists to examine the generality of the associated explanatory mechanisms. Even where phenomena seem to mismatch, closer analyses may reveal deeper relationships or fundamental differences. Finally, comparing and contrasting similarity and choice may serve to highlight mechanisms that would not be salient in either domain considered by itself. In this paper, we first lay out a series of correspondences between similarity and decision making, and then examine the degree to which these parallels suggest that decision making and similarity judgments involve common processes. Finally, we speculate on the degree to which similarity judgments and decision making may be viewed as two manifestations of the same process. PARALLEL PHENOMENA It will be useful to imagine some generic choice context to motivate our discussion. Consider a situation in which there are three candidates for a teaching position and the decision must be made as to who to interview first (resources are limited, so it is not feasible to interview all three) on the basis of their résumés. First of all, one would need to determine the types of information such as teaching experience and amount of education that are relevant to this decision. The résumés would presumably provide specific information or values on these dimensions, and they may even serve to suggest relevant dimensions. Next, the candidates would be compared along these relevant dimensions. Of course, the résumés may not be perfectly comparable, as one may list information (e.g., hobbies, teaching ratings) not included in others. This information must then be integrated in some form to arrive at a decision. To modify the context in the direction of similarity judgments, imagine that the candidates are being compared with some previous teacher, and that the question concerns which of the three candidates is most similar to that teacher. Of course, if one résumé were outstanding and the others mediocre, the decision would be easy. In many choice contexts, however, one faces tradeoffs across relevant dimensions; one candidate, for example, may have more education but less experience than another. One might think that one should simply weight dimensions according to their importance and select the candidate whose (weighted) overall impression is the highest. There

3 SIMILARITY PROCESSES AND DECISION PROCESSES 3 is abundant evidence, however, that the weights assigned to dimensions depend importantly on the context and the set of candidates under consideration. We begin our analysis with factors or processes associated with weighting of dimensions in both similarity and choice. Weighting A number of distinct subprocesses have been identified that influence or determine the weights associated with features or dimensions. Cumulatively, these subprocesses suggest that preferences (including similarity judgments) are not simply prestored and retrieved but, rather, are at least partially constructed in the choice context. S R Compatibility, Preference Reversals, and Framing It is now well established that different measures of preference may disagree with one another. For example, Lichtenstein and Slovic (1973) gave people a choice between bets that involved a high probability of winning a relatively small number of chips (e.g., an 11/12 chance of wining 12 chips, a 1/12 chance of losing 24 chips) or a low probability of winning a larger number of chips (e.g., a 2/12 chance of winning 79 chips, a 10/12 chance of losing 5 chips); the chips could be exchanged for money. They found that, generally, people were roughly indifferent between these two bets but placed a higher selling price on the second bet than they did on the first, regardless of whether they chose the first or the second. These preference reversals are robust, despite their incompatibility with rational choice (e.g., Grether & Plott, 1979). Tversky, Sattath, and Slovic (1988) have offered an account of these results in terms of a compatibility principle. Their idea is that the weight given to a dimension depends on how compatible it is with the judgmentresponse scale that is being used to assess preference. Asking people to assign a dollar value to a bet favors attention to the amount of money associated with a bet. Tversky et al. provided a number of demonstrations that the weight of a choice dimension is enhanced when it is compatible with the assessment dimension. Goldstone (1993) obtained an analog of the compatibility effect in a numerosity estimation task. When subjects were shown the two displays in Figure 1 and asked to select the display with a greater percentage of white squares, they had a tendency to select the display on the right. Surprisingly, another group of subjects had a tendency to select the right display as possessing a greater percentage of black squares. Other experiments showed that this intersubject inconsistency is due to a selective weighting of display regions that contain a high concentration of features that are mentioned in the instructions as the basis for the response. For example, if subjects are instructed to choose the display that contains more white squares, they are highly influenced by squares that come from regions with many white squares. Thus, the scene with clusters of black and white squares may appear to Figure 1. Stimuli used by Goldstone (1993). There is a tendency for subjects to select the display with clustered regions of black and white squares as possessing a greater percentage of both black and white squares. contain a greater percentage of both black and white squares, depending on what features are emphasized by the instructions. There are corresponding compatibility effects in similarity. One parallel derives from Tversky s (1977) contrast model, which assumes that similarity is a weighted function of matching (i.e., common) and mismatching features. Tversky suggested that, compared with similarity judgments, difference or dissimilarity judgments give relatively less weight to common features and more weight to distinctive features. He tested this idea using pairs of stimuli in which one pair had more features (both common and distinctive) than the other (that is, people knew more about one pair than about the other). An example from Tversky involves the pairs {East Germany, West Germany} and {Ceylon, Nepal}. Tversky found that 67% of participants rated the two Germanys as more similar than Ceylon and Nepal, while 70% of a second group rated the two Germanys as more different. This finding is consistent with the suggestion that relative to similarity judgments, difference judgments preferentially weight mismatching features. In a similar study, Shafir (1992) set up a choice situation in which parents were competing for custody of a child. One parent had both more positive and more negative qualities than the other. One group of participants was asked which parent should be awarded custody, and a second group was asked which parent should not be awarded custody. To a reliable extent, both groups selected the same parent namely, the one with more positive and negative qualities (see Shafir, 1993, for other examples and further discussion). Value-Specific Weighting and the Max Principle Another finding common to both choice and similarity is that the weight attached to a dimension is not necessarily independent of its value and the overall context. Goldstone, Medin, and Gentner (1991) found violations of independence in similarity judgments in their studies evaluating the relative contributions of attributes (one-

4 4 MEDIN, GOLDSTONE, AND MARKMAN place predicates, such as white ) and relations (two- or more-place predicates, such as white triangle above red circle ) to similarity judgments. They found that the impact of an added feature on similarity was heightened when the compared objects had other matching features of a similar type (e.g., an attributional match received more weight when the objects were attributionally similar, but a relational match was relatively more important when the objects were relationally similar). They referred to this as a max principle that is, whichever aspect of similarity maximizes similarity receives more weight. Rubinstein (1988) has suggested that a similaritybased process that leads to violations of independence can account for the common-ratio effect in choice behavior. For example, consider the following choices between A and B and between C and D: A: ($3,000,.90; $0,.10) vs. B: ($6,000,.45; $0,.55); C: ($3,000,.02; $0,.98) vs. D: ($6,000,.01; $0,.99). Choice A is interpreted as a 90% chance of winning 3,000 dollars and a 10% chance of winning nothing. By the independence axiom, people should either choose A and C or B and D. (For both choices, one alternative offers twice the amount of money as the other choice, but with only half the probability of winning the money.) In opposition to the independence axiom, the majority of people given these gambles choose A over B, and D over C. Rubinstein s (1988) conjecture is that the difference between the two choice settings is that in C versus D, the probabilities are similar (.01 vs..02), and that therefore more weight is given to amount (which favors D). Shafir, Osherson, and E. E. Smith (1993) have proposed a descriptive account of choice that weights both relative probabilities as well as absolute differences in probability, allowing the model to account for many violations of the independence axiom, including Rubinstein s results. Both ideas accomplish value-specific weighting. Intransitivities in a set of choices provide another example of attribute weighting that depends on the set of compared entities. Tversky (1969) presented participants with a series of choices like the ones in Table 1, in which Choice A, for example, represents a 7/24 chance of winning $5 and a 17/24 chance of winning $0. He observed the following intransitivities: People preferred A to B, B to C, C to D, and D to E, but they preferred E to A. One interpretation of this result is that only differences along a dimension that exceed a certain criterion may be registered as important. Small differences along Table 1 Choice Set Used by Tversky (1969) A ($5.00, 7/24; $0, 17/24) B ($4.75, 8/24; $0, 16/24) C ($4.50, 9/24; $0, 15/24) D ($4.25, 10/24; $0, 14/24) E ($4.00, 11/24; $0, 13/24) Figure 2. Stimuli used to examine intransitivities in similarity judgments. In successive forced-choice judgments between pairs of objects, there is a tendency for subjects to select B over A, C over B, and A over C as more similar to the standard. an important dimension are edited out or ignored. While probability information is ignored when adjacent options are compared, it is considered fully when Choices A and E are compared. Two of the present authors (Goldstone & Medin) have recently completed a similarity-judgment study modeled after an example from Arrow (1951) involving paradoxes associated with voting aggregation. In this more recent study, people are asked which of two alternatives is more similar to the standard. As illustrated in Figure 2, the standard is compared to Items A, B, and C. In general, when any two alternatives are presented, subjects can choose either the item that is closer to the standard on two out of three dimensions (a number-ofdimensions strategy) or the item that is much closer to the standard on the dimension with the largest difference (a largest-dimensional-difference strategy). For example, B is much closer to the standard than is A on the dimension with the largest difference that of angle but A is somewhat closer than B on the other two dimensions. Consistent application of either of the above strategies would result in systematic intransitivities. Using largest dimensional difference as the criterion, B should be chosen over A, C over B, and A over C. Using number of dimensions as the criterion, exactly the opposite pattern should be obtained. The particular dimension values were customized for each individual subject, so that angle, size, and color differences were approximately equally salient. The results showed systematic intransitivities with both strategies, with more intransitivities in accordance with the largest-dimensional-difference strategy. The number of choices (out of a total of 144) consistent with a largest-dimensional-difference strategy was computed for each of the subjects. If subjects showed no susceptibility to intransitivities, the expected frequency of largestdimensional-difference responses would follow a binomial

5 SIMILARITY PROCESSES AND DECISION PROCESSES 5 distribution with a mean of 72. If there are no intransitivities in similarity, we would expect very few subjects (fewer than 1 out of the 58 tested subjects) to produce more than 90 or fewer than 54 largest-dimensionaldifference responses. In contrast to this prediction, quite a few subjects (n 20) made more than 90 such responses, and some (n 4) made fewer than 54. The prevalence of intransitive responses in similarity judgments parallels the intransitivity found in decision making. In both cases, a large difference between choices on a dimension is more influential than is expected by the additive effect of smaller differences on the same dimension. More generally, these results show statistically reliable intransitivities, consistent with value-specific dimension weighting in both similarity and choice contexts. Choice Similarity Tversky s pioneering studies of the dynamic character of similarity (Tversky, 1977; see also Tversky & Gati, 1978) included the idea that categorization affects similarity. This idea, referred to as the diagnosticity hypothesis, is that features used as the basis for categorization acquire diagnostic value and increase the similarity of the objects that share them. This concept may be simply operationalized as follows: In one condition, participants are asked to sort stimuli into groups of equal size, and in another, participants are asked to make similarity judgments. For example, given the set consisting of Israel, Syria, Iran, and England, 72% of the participants put Israel and England into the same category, but given the set consisting of Israel, France, Iran, and England, only 16% put England and Israel together. In the similarity-judgment condition, subjects decided which of the three countries was most similar to a standard (Israel). The percentage of times each country was selected as most similar to Israel is shown in the top sets in Table 2. The relative choices of England versus Iran shifted as a function of the comparison context. One measure of diagnosticity consists of the percentage of choices of the diagnostic alternative (as defined by the sorting task [i.e., England in Set 1 and Iran in Set 2] as being most similar to the standard) minus the percentage of choices of the nondiagnostic alternative; that is, (38% 38%) (46% 24%) 22%. The middle sets of Table 2 show results from another pair of contexts which yielded an even larger diagnosticity effect (59%). Overall, Tversky and Gati (1978) found a reliable diagnosticity effect (using this measure) across 20 sets of countries. Glucksberg and Keysar (1990) also reported reliable diagnosticity effects with literal and metaphorical contexts (see the bottom sets in Table 2, which show a 34% diagnosticity effect). Tversky s (1977) interpretation of these effects is that changes in feature salience modify the importance of particular matching and mismatching features. In Glucksberg and Keysar s (1990) study, for example, in the context including pimples, the feature corresponding to artifact versus natural would be salient, whereas in the context including statues, the feature corresponding to attractiveness versus ugliness would be salient. Suppose, however, that we view these context effects from the perspective of decision making. Consider the idea that the middle context item is an alternative that competes with the other items to be selected. That is, one could think of the diagnosticity contexts as a way of examining similarity effects in choice (as in studies aimed at demonstrating violations of Luce s [1959] constantratio rule [Tversky, 1972]). In this case, the middle item should take more choices from the alternative that is similar to it than from the alternative that is dissimilar to it. In the domain of decision making, this pattern of data is referred to as a substitution effect. For example, one could view the results shown in the last sets in Table 2 as indicating that pimples take choices that would have gone to warts and that statues takes choices that would have gone to paintings. This prediction is made by Tversky s elimination-by-aspects (Tversky, 1972) and preferencetree (Tversky & Sattath, 1979) models. In both models, each choice is represented as an ensemble of aspects, and at each stage in the decision, one eliminates all of the choices that do not have a selected aspect. Pimples takes more choices from warts than from paintings because pimples and warts would both be candidates if the ugly feature were selected as the basis of choice, but if the ar- Table 2 Examples of Diagnosticity Sets Taken from Tversky and Gati (1978), Tversky (1977), and Glucksberg and Keysar (1990) Set 1 Set 2 Standard Stimulus Judged Most Similar * Standard Stimulus Judged Most Similar * 1. Israel England 38 Israel England 24 Syria 24 France 30 Iran 38 Iran Austria Sweden 49 Austria Sweden 14 Poland 15 Norway 26 Hungary 36 Hungary Billboards Paintings 58 Billboards Paintings 33 Pimples 11 Statues 27 Warts 31 Warts 40 *Percentage of participants who judged the stimulus to be most similar to the standard for that set.

6 6 MEDIN, GOLDSTONE, AND MARKMAN tifact feature were selected, paintings would have no remaining competitor. How can one determine whether there are diagnosticity effects over and above the substitution effects predicted by these models? A conservative criterion is that the choices of the diagnostic alternative in the two contexts must sum to greater than 100%. For instance, in the billboards example, if the sole function of pimples were to take choices from warts, the absolute number of choices of paintings should not be enhanced and the same should hold for choices of warts in Set 2. Using the 100% criterion would rule out any contribution of substitution effects, but would likely underestimate diagnosticity effects. Unambiguous evidence for enhancement is found in the sets of countries in the middle groups of Table 2, in which Poland and Hungary together account for 51% of the choices in Set 1, while Hungary alone accounts for 60% of the choices in Set 2. In this case, the increase in choice of Hungary when it is the diagnostic alternative cannot be explained in terms of lack of competition from Poland because that factor could only account for up to 51% of the choices. Overall, the diagnostic alternative is selected for a total of 109% (49% 60%). Note, however, that the corresponding sums in the top and bottom sets in Table 2 are 84% and 98%, respectively both less than the 100% criterion. Since Tversky and Gati (1978) reported only the diagnosticity scores for the other 18 country comparisons, it is not possible to determine whether there is a diagnosticity effect that cannot be attributed to substitution. Recently, Medin and Kroll (1994) examined diagnosticity effects using geometric forms having as stimuli varying degrees of attributional and relational similarity. For example, in Figure 3, Set 1, A shares the relation same shading, and C the relation above, with the standard. The third choice, B, varies across sets such that C should be the diagnostic alternative in Set 1 and A the diagnostic alternative in Set 2. Participants were asked to rank order the similarity of the alternatives with respect to the standard. Overall, the diagnostic alternative was ranked above the nondiagnostic alternative 55% of the time, a reliable effect. The relative ranking measure eliminates the context (B) item from consideration, and therefore the diagnosticity effect is not attributable to substitution. In short, it appears that there are diagnosticity effects that cannot be explained in terms of substitution; however, as we shall shortly see, there may be other interpretations of diagnosticity. Attraction, Compromise, Diagnosticity, and Reasons Attraction. A paradoxical finding has recently been uncovered in the decision-making literature. Specifically, adding an alternative similar to one item from the original choice set may actually boost choices of that original-choice item (Huber, Payne, & Puto, 1982; Huber & Puto, 1983; Simonson & Tversky, 1992). This phenomenon (the attraction effect) violates the assumption of regularity (i.e., that adding a new alternative cannot increase the probability of choosing a member of the original set), which is crucial for the validity of most probabilistic-choice models. Figure 4 (for the moment ignoring Item T) illustrates the conditions under which attraction effects are reliably obtained. The key feature is that the added alternative (C or D) is asymmetrically dominated by one of the original choice options (namely, the most similar one). Adding C increases the number of times A is chosen, and adding D increases the number of times B is chosen, relative to original (A,B) choice context. Huber and Puto (1983) found that an added alternative could produce attraction effects when it was simply relatively inferior and technically not asymmetrically dominated. What is responsible for attraction effects? Several decision researchers have advanced the idea that when preference is uncertain (i.e., no dominating alternative is present), choices may be determined not by direct preferences but rather by the justifications or reasons for choosing or avoiding alternatives (Montgomery, 1983; Figure 3. Sample stimuli from the study of diagnosticity effects using relational properties. In Set 1, Choice C is the only alternative that shares an above relation with the standard. In Set 2, Choice A is the only alternative that shares a same-shading relation with the standard.

7 SIMILARITY PROCESSES AND DECISION PROCESSES 7 Figure 4. Paradigm for attraction effects. Shafir & Tversky, 1992; Slovic, 1975; Slovic, Fischhoff, & Lichtenstein, 1982). Simonson (1989) suggested that attraction effects may be mediated by the fact that the decision maker notes that one choice clearly dominates at least one of the alternatives, providing a simple reason for selecting the dominating alternative. In support of that hypothesis, Simonson found that attraction effects were reliably larger when people knew they would have to justify their choices than when they knew they would not have to justify their choices. Aakers (1991) also found an attraction effect under high-justification conditions (see also Heath & Chatterjee, 1991; Ratneshwar, Shocker, & Stewart, 1987, for other relevant observations concerning attraction effects). Interestingly, however, Aakers observed negative attraction under conditions of low justification. Although there are numerous differences between Simonson s (1989) and Aakers (1991) studies that may account for the differing results under low justification, we wish to call attention to the fact that negative attraction in choice corresponds to true diagnosticity effects in similarity judgments (Aakers ruled out substitution effects by using a rating measure). That is, if we make a correspondence between similarity and preferability, a negative attraction effect would be analogous to Tversky s (1977) observed diagnosticity effect. These parallels lead to the speculation that attraction effects could be obtained in similarity judgments. Figure 4 shows a straightforward way to map the preference task onto similarity judgments. The task is to indicate which alternative (A or B) is most similar to the standard (T), where the choice context includes either C or D. Interestingly, attraction effects in similarity judgments would likely correspond to negative diagnosticity effects, because B and D would be likely to be sorted together in the set consisting of A, B, D, and T, while A and C would likely be put in the same category for the set A, B, C, and T. Using essentially this design, Medin, Pineda, and Markman (1994) have obtained very strong attraction effects in similarity judgments. Compromise. Simonson (1989) provided further evidence for the importance of justification in judgments by demonstrating another interaction between the items in a choice set. Consider a situation with nondominated alternatives, A and B, in which a third option, C, is added that is least favorable on one dimension and most favorable on the other dimension (see Figure 5). Simonson reasoned that in this context, the alternative most similar to the new choice (in this case, B) might be selected with the justification that it now represents a compromise between alternatives that are high on one dimension and low on the other. He observed reliable compromise effects that increased when people knew that they would have to justify their choices. As in the case of attraction effects, one can test for compromise effects in similarity judgments by creating a standard and a set of alternatives. For example, if some standard high on both dimensions were added to Figure 5, one might anticipate that the probability of choosing B as most similar to T in the choice set consisting of A, B, and C might be greater than when the choice set is restricted to just A and B. Again, Medin et al. (1994) have recently observed reliable compromise effects in similarity judgments. Diagnosticity revisited. Consider Figure 3 again and imagine that participants are asked to select the alternative that is least similar to the standard. According to the diagnosticity hypothesis, an alternative should be less likely to be selected as least similar when it shares diagnostic features with the target. A contrasting prediction can be derived from the idea that people want a reason to justify their judgments (Simonson, 1989). For instance, given Set 1 from Figure 3, a reason to pick C as most different is that it is the only alternative not having the relation same shading. In Set 2, A is the only choice not having the relation above. In short, the wanting a reason view leads to the prediction that diagnostic alternatives may be picked both as most similar to and as most different from a standard. In preliminary observations, Medin and Kroll (1994) have found that the diagnostic alternative is selected as most differ- Figure 5. Paradigm for compromise effects.

8 8 MEDIN, GOLDSTONE, AND MARKMAN ent for a mean total of 104%, consistent with the idea that reasons are guiding judgments. (This figure is not reliably above 100%, so these data can only be taken as suggestive.) In choice contexts in which substitution effects are found, one wonders what might happen if participants were asked which alternative they least preferred. If people are looking for justifications for their judgments, adding an alternative Z similar to X might lead to more choices of Y as least preferred, compared with the number of times Y is chosen in the two-alternatives (X vs. Y) choice context. Summary of Weighting Effects So far, our review has suggested that the weighting of dimensions is dynamic and context dependent for both similarity and choice. Furthermore, the processing principles underlying weighting appear to be comparable at a more specific level of detail (e.g., compatibility, reasons). We turn now to questions of comparability or alignability of choices, a process which has often been taken for granted in both domains. As we shall see, current work reveals the dynamic character and importance of comparison processes. Alignment and Comparison Common Currency Early work in both similarity judgments and decision making made an assumption of common currency, according to which all factors can be framed in comparable units. For decision making, the units are utilities, and it was assumed that all costs and benefits could be translated into utilities. In similarity judgments, the common metric was either distance (for multidimensional scaling) or featural overlap (for feature-based models). One problem with this view is that not all comparisons are equally easy to make; comparisons that involve substantially different properties are difficult. It is easier, for example, to compare the merits of Mendelssohn and Schumann than to compare the merits of Schumann and the Beatles. It may be possible to convert both Schumann and the Beatles into generic utilities, but this process seems to require more work than comparing items that have similar aspects. This example provides an initial indication that decision making may not proceed by automatically converting alternatives into a generic metric. Framing effects also suggest that choices are not converted into a generic metric. When bidding for the opportunity to play a gamble, the potential gain from the gamble is emphasized; when choosing between gambles, the probability of winning is emphasized. If alternatives were automatically converted into utilities, information about how the utility was achieved (e.g., high probability vs. high potential gain) would be discarded. Context and framing effects eliminate the possibility of creating simple translations between aspects. For example, a statement that applies in the bidding scenario, such as increasing the probability of winning by 5% is equal to a $10 increase in payoff, will not apply in the choice situation. Likewise, in similarity judgments, the prospects for a single currency are not encouraging. As William James (1892/1989) pointed out, the moon is like a ball (because both are round), and the moon is like a lamp (because both are bright), but a lamp and a ball are not at all similar. Tversky and Gati (1982) presented a number of similar examples as demonstrations of violations of the metric axioms underlying mental-distance models of similarity. Fillenbaum and Rapoport (1974) asked a linguist for similarity ratings between verbs. From these data, they argued that the linguist had many similarity criteria, and that the criteria used for a given judgment depended on the particular items being compared. For example, acquit was judged to be similar to clear because both are synonyms; acquit was judged to be similar to convict because both are alternatives from the same class; and apologize was judged to be similar to forgive because one has the other as its goal. Likewise, different methods for obtaining comparison data reveal different values. For example, shared features are more important for similarity ratings, while unique features are more important for dissimilarity ratings (e.g., Gati & Tversky, 1982). Thus, we cannot construct a generic translation such as two shared features are as influential as three distinctive features. A generalization of many of the results from the literature on similarity judgments and on decision making is that comparisons tend to be made at the most concrete level possible (e.g., Payne & Bettman, 1992). Abstract values can be assigned to dimension values, but this takes effort and may not be intuitive. If possible, items are compared on the basis of specific features, such as A has more years teaching experience than B. Only when required by lack of agreement on particular dimensions do comparisons involve abstract assessments of the overall value of items. Structural Alignment, Similarity Judgments, and Decision Making It seems fairly uncontroversial that when one assesses a bet, one compares probabilities with probabilities and amounts with amounts, and that when one judges forms varying in color and shape, one compares colors with colors and forms with forms. Recent studies of similarity have led to the outlines of a process model for comparison (Gentner & Markman, in press; Goldstone, 1994b; Goldstone & Medin, 1994a, 1994b; Markman & Gentner, 1993a; Medin, Goldstone, & Gentner, 1993). According to this view, similarity comparisons involve a process of structural alignment akin to the one proposed to mediate analogical reasoning (Gentner, 1983, 1989). Briefly, this view assumes that objects (or choices) are represented by hierarchical relational structures that explicitly encode relations between dimensions as well as connections between dimensions and their values.

9 SIMILARITY PROCESSES AND DECISION PROCESSES 9 The output of the comparison process consists of a set of commonalities as well as two kinds of differences alignable differences and nonalignable differences (Markman & Gentner, 1993a). Alignable differences are related to the commonalities of a pair; that is, two choices having different values along a common dimension (e.g., different prizes in two lotteries) would constitute an alignable difference. In contrast, nonalignable differences are unrelated to the commonalities of a pair; that is, one choice having a value along a unique dimension would constitute a nonalignable difference. Structural alignment has two key aspects that are important for this discussion. First, it predicts that cognitive processes should treat alignable and nonalignable differences in different ways; and second, it suggests that similarity (patterns of matching and mismatching attributes and relations) and alignment interact dynamically. These predictions have been tested directly in the similarity literature, and we will first present a discussion of some of this research. Following that, we will present some phenomena in decision making that we think are compatible with this view of comparison. Alignment in similarity. Much evidence suggests that the structural-alignment process entails global constraint satisfaction rather than local matching (e.g., Falkenhainer, Forbus, & Gentner, 1989; Medin et al., 1993). For example, Markman and Gentner (1993b) asked people to point to the feature in one scene that went best with a specified feature in a second scene. People tended to select the most similar object from the other scene. However, if people first made similarity judgments before being asked to point to correspondences, their choices were based on the object in the second scene that played the same role as the object in the first scene. In other work, Goldstone and Medin (1994a, 1994b) required participants to make similarity or sameness difference judgments under different deadlines. For short deadlines, performance was a function of the total number of matches between the stimuli being compared. At longer deadlines, performance was increasingly likely to be a function of matches in corresponding roles and relations rather than of just the sheer number of matches. Although there is a sense in which feature-matching models like Tversky s (1977) contrast model perform alignments between features, current evidence points to the need for detailing and examining the implications of the alignment processes. While the contrast model might be said to align common features, evidence suggests that the extent to which two common features are placed in alignment depends on whether they are consistent with (and connected to) other alignments that are simultaneously being created (Clement & Gentner, 1991; Goldstone, 1994b; Markman & Gentner, 1993a). In order to know how important a particular shared feature is for increasing similarity, one must know how similar the parts are that possess the shared features, how similar other pairs of parts are, and which part-to-part alignments are (in)consistent with other part-to-part alignments. That is, alignment is based on global constraint satisfaction rather than on the best local matches. Markman and Gentner (1993b) provided specific evidence for the distinction between alignable and nonalignable differences in comparisons. Participants were asked either to list commonalities and differences of word pairs or to rate their similarity. The pairs were selected so as to differ widely in their similarity. The two findings of particular interest are that, as indicated by regression analyses, alignable differences and nonalignable differences were given different weight in reducing similarity, and that the kinds of differences listed for a pair depended on the similarity of the words in the pair. Similar pairs had more listed alignable differences than did dissimilar pairs, but they also had fewer listed nonalignable differences than did dissimilar pairs. These observations both reinforce the role of alignment in comparisons and indicate the need to distinguish between alignable and nonalignable differences. Finally, these results suggest that the ease of comparison affects the availability of alignable differences, which in turn affects similarity or other processes (such as choice) that involve comparisons. Alignment in choice. Although structural alignment has not been tested explicitly in a decision-making context, there is some evidence that alignment affects choice behavior. For example, Table 3 shows a pair of complex options studied by Tversky and Kahneman (1986). Participants were told that each option corresponded to a separate box of marbles with the proportion of different colors and associated outcomes as shown in the table. Separate groups were shown either A and B or C and D. If corresponding colors are aligned, it is easy to see that Option A dominates Option B, the only differences being the outcomes associated with a green or blue marble. Option C in the second gamble can be created by painting the green marble red and the blue marble green, while leaving the payoffs attached to each marble unchanged. Similarly, Option D can be created from B by painting the blue marble yellow and leaving the payoffs intact. In short, the overall probabilities and payoffs are identical for A and C and for B and D, and, therefore, Option C dominates Option D just as Option A Table 3 Choice Options Used by Tversky and Kahneman (1986) Marbles (%) Option White Red Green Blue Yellow A Outcome $0 Win $45 Win $45 Lose $10 Lose $15 B Outcome $0 Win $45 Win $30 Lose $15 Lose $15 C Outcome $0 Win $45 Lose $10 Lose $15 D Outcome $0 Win $45 Win $30 Lose $15

10 10 MEDIN, GOLDSTONE, AND MARKMAN dominates Option B. Note, however, that if matching colors are aligned, the biggest difference in the values of corresponding dimensions is now associated with the green marble, for which Option D has a much more favorable outcome. The participants in the group presented with the first gamble all chose A over B, but a majority (58%) of the participants presented with the second gamble chose D over C. In this case, the most natural form of alignment has a striking effect on choices. Johnson (1989) presented evidence that subjects decisions are more likely to involve attributes of the objects when the items are easily alignable. Thus, when choosing between two toasters, the subject may explicitly consider the number of slots that each one has. In contrast, when selecting between a toaster and an iron, the number of slots in the toaster is no longer important; rather, subjects may focus on other issues, such as how much they need a toaster versus how much they need an iron. The importance of a feature in making a decision depends on whether the choices can be compared on the feature (see also Johnson, 1984, 1986). Russo and Dosher (1983) presented a similar argument to suggest that dimensional processing of alternatives will be preferred to holistic processing when the dimensions are easily compared, because dimensional processing often requires less effort. Payne (1982, Payne & Bettman, 1992) has suggested that the differing results from choice and judgment paradigms can be understood within the framework of similarity models. His idea is that in judgment contexts, people consider both common and distinctive features, while in choice contexts, they focus on distinctive features. People can make decisions either by comparing whole items to each other (holistic processing) or by comparing items feature by feature (attribute-based processing). Expected-utility theory assumes holistic processing; for example, if a person is deciding between a vacation in Africa and a vacation in Europe, in accordance with this theory, the expected utility of each vacation would be determined separately, with all of its attributes and their importance being taken into account. However, researchers have observed that people often use attribute-based processing (Hogarth, 1980; Payne, 1976; Russo & Dosher, 1983). According to what Hogarth calls the additive-difference model, people make choices by comparing items on selected attributes; using this technique, a person might reason, Africa would be more of an adventure and would be a more memorable experience; Europe would be culturally more interesting. This technique involves aligning the choices on dimensions. Payne found that this alignment strategy is particularly prevalent when people have many alternatives to examine and each alternative has many features. Hogarth observed that the additive-difference technique can considerably ease information-processing demands since it involves comparing information that is commensurable (p. 75). Decision-making work in the area of mental accounting also supports an alignment process. The basic notion of mental accounting is that people establish separate budget entries for different types of costs, and that they prefer to compare items within these types (Thaler, 1985). Even when all entries involve the same type of cost (e.g., money), there is a tendency to compare equivalent entries. For example, Kahneman and Tversky (1984, p. 347) gave subjects the following scenario: Imagine that you are about to purchase a jacket for $125 and a calculator for $15. The calculator salesman informs you that the calculator you wish to buy is on sale for $10 at the other branch of the store, located 20 minutes drive away. Would you make a trip to the other store? Subjects are more willing to make the trip in this scenario than in a scenario where the calculator is $125 ($120 on sale) and the jacket is $15. According to subjective-utility theory, these decisions should be equivalent, both trading off $5 saved on a purchase total of $140 for a 20-minute trip. Instead of tabulating total cost, people seem to align comparable items and compare their prices. When calculators are aligned with calculators (and jackets with jackets), the difference between $10 and $15 seems more impressive than the difference between $120 and $125. Even within a pair of choices, the relative attention given to comparable and noncomparable dimensions may be important. For example, Slovic and MacPhillamy (1974) asked participants to rate students who had scores on one common dimension (e.g., English skills) and one unique dimension (e.g., achievement need for one student and quantitative skills for the other). When a dimension was common, it received much more weight than it did when it was unique. Cautioning participants not to increase the weight of the common dimension did not reduce the effect. Alignment of choices may also underlie a well-known violation of expected-utility theory s substitutability assumption. According to substitutability, if Options A and B are equally preferred, and Options A and C are equally preferred, Options B and C should be equally preferred. However, one can imagine a situation where a trip to Rome (Option A) and a trip to Paris (Option B) are equally attractive. Furthermore, if these trips are equally preferred, it is reasonable to think that the choice between a trip to Paris plus one dollar (Option C) and a trip to Rome is just as difficult to make. One would expect the addition of one dollar to be almost completely insignificant for the decision. However, given a choice between a trip to Paris and a trip to Paris plus one dollar, the latter alternative strongly dominates. This result is predicted from an alignment perspective. The choice between Paris and Paris $1 involves items that are easily placed in alignment. When the two Paris aspects are aligned, the remaining $1 of Option C is salient. Greater sensitivity for detecting utility differences in choices is predicted if the choices can be aligned. The idea that people align and compare specific features is, of course, the basis for the effects of choice similarity described earlier in this paper. In Tversky and Sattath s (1979) preference-tree model (a specialization of